# Thread: Bacteria growth question with formula

1. ## Bacteria growth question with formula

2. Originally Posted by aikenfan
First, we need to find k

(Note that 100 is the initial size)

We are told when N = 300, t = 5, so plug those in:

$\displaystyle \Rightarrow 300 = 100e^{5k}$

Now solve for k.

Once you have k, put it in the original formula. then plug in N = 200 and solve for t, that will give you the required time

Any questions?

3. i get .2197 for k
do i have to double the 300 as well or just the 100?

4. Originally Posted by aikenfan
i get .2197 for k
correct!

do i have to double the 300 as well or just the 100?
now that we know k, we have:

$\displaystyle N = 100 e^{0.2197t}$

now plug in N = 200 (since that is double 100 -- the initial population size) and solve for t

you were just given the 300 to find k, now that you have, forget about it. i believe the question is asking how long it takes to double from the initial population (i may be wrong)

all i know, you only have to use one or the other, not both. if you want to find how long it takes to double from 300, then plug in N = 600 and solve for t, then subtract 5 from the answer

5. why do i subtract 5?

6. Originally Posted by aikenfan
why do i subtract 5?
i was thinking they would want the time required to double, since it was 300. it was 300 at 5 seconds, so to find the additional seconds, need to subtract 5 from the total time it took to get to 600